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  "body": "\n## Summary\n\nAn abelian scheme over a base scheme $S$ is a family of [[abelian varieties|R7W03TXRS9]] parametrized by $S$.\nIt is a smooth proper [[group scheme|TJ04VQP4NB]] over $S$ with geometrically connected fibres.\nAbelian schemes describe abelian varieties with good reduction, and they are the objects classified by moduli spaces of abelian varieties.\n\n## Explanations\n\n### L1 human\n\nAn abelian variety is a single geometric object with an addition law.\nAn abelian scheme lets this object vary with a parameter, like a whole family of elliptic curves.\nOver the integers, the parameter is a prime $p$, and the fibre at $p$ is the reduction of the variety modulo $p$.\nFor example, the curve $y^2 = x^3 - x$ gives an abelian scheme over $\\Z[1/2]$, because it stays smooth modulo every odd prime.\n",
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